7.2 Result
7.2.1 Results on real-valued MRI data
Figure 45: PSNR curves of RefineGAN with different undersampling rates on the brain training set over 500 epochs.
and the second check point in our two-fold chaining network asRefineGAN. The entire chaining structure (with 2 generators) is trained together. Each individual cycle has its own variable scope and hence, their weight are updated differently. The later structure serves as a boosting module which improves results.
(a) 10% (b) 20% (c) 30% (d) 40%
Figure 46: Radial sampling masks used in our experiments.
Table 13: Running time comparison of various CS-MRI methods (in seconds).
Abbreviation Methods Brain Chest CSCMRI [101, 102] 8.56808 9.37082
DLMRI [18, 19, 104] 604.24623 613.84531
DeepADMM [117] 0.31725 0.28677
DeepCascade [110] 0.22182 0.25627
SingleGAN [91, 134] 0.064599 0.075529
ReconGAN — 0.060753 0.068871
RefineGAN — 0.106157 0.111607
we randomly selected 100 images for training the network and another 100 images for testing (validating) the result. We conducted the experiments for various sampling rates (i.e., 10%, 20%, 30%, and 40% of the original k-space data), corresponding to 10×, 5×, 3.3×, and 2.5×factors of acceleration. We assume the target MRI data type is static, and radial sampling masks are applied (Figure 46). It is worth noting that our experimental data are real-valued MRI images, which require pre-processing of the actual acquisition from the MRI scanner because the actual MRI data is complex-valued. Additional data preparation steps, such as data range normalization and imaginary channel concatenation, are also required.
Running Time Evaluation: Table 13 summarizes the running times of our method and other state-of-the-art learning-based CS-MRI methods. Even though dictionary learning-based approaches leverage pre-trained dictionaries, their reconstruction time depends on the numerical methods used. For example, CSCMRI by Quan and Jeong [101, 102] employed a GPU-based ADMM method, which is considered one of the state-of-the-art numerical methods, but the running time is still far from interactive (about 9 seconds). Another type of dictionary learning-
(a) Brain 10% (b) Chest 10%
(c) Brain 20% (d) Chest 20%
(e) Brain 30% (f) Chest 30%
(g) Brain 40% (h) Chest 40%
Figure 47: PSNRs evaluation on the brain and chest test set. Unit: dB
(a) Brain 10% (b) Chest 10%
(c) Brain 20% (d) Chest 20%
(e) Brain 30% (f) Chest 30%
(g) Brain 40% (h) Chest 40%
Figure 48: SSIMs evaluation on the brain and chest test set
(a) Brain 10% (b) Chest 10%
(c) Brain 20% (d) Chest 20%
(e) Brain 30% (f) Chest 30%
(g) Brain 40% (h) Chest 40%
Figure 49: NRMSEs evaluation on the brain and chest test set
FullRecon ZeroFilling DLMRI CSCMRI DeepADMM DeepCascade SingleGAN ReconGAN RefineGAN
0 20 40 60 80 100 120 140 160
(a)
FullRecon ZeroFilling DLMRI CSCMRI DeepADMM DeepCascade SingleGAN ReconGAN RefineGAN
0 50 100 150 200 250
(b)
Figure 50: Image quality comparison on the brain (a) and chest dataset (b) at a sampling rate 10% (top 3 rows) and 30% (bottom 3 rows): Reconstruction image, zoom in result and 10×
error map compared to the full reconstruction.
based method, DLMRI [18, 19, 104], solely relies on the CPU implementation of a greedy algorithm, so their reconstruction times are significantly longer (around 600 seconds) than those of the others with GPU-acceleration. Deep learning-based methods, including DeepADMM, DeepCascade, and our method, are extremely fast (e.g., less than a second) because deploying a feed-forward convolutional neural network is a single-pass image processing that can be ac- celerated using GPUs reasonably well. DeepADMM significantly accelerated time-consuming iterative computation to as low as 0.2 second. The running times of SingleGAN [91, 134] and our ReconGAN are, all similarly, about 0.07 second because they share the same network archi- tecture (i.e., single-fold generator G). The running time of RefineGAN is about twice as long because two identical generators are serially chained in a single architecture, but it still runs at an interactive rate (around 0.1 second). As shown in this experiment, we observed that deep learning-based approaches are well-suited for CS-MRI in a time-critical clinical setup due to their extremely low running times.
Image Quality Evaluation: To assess the quality of reconstructed images, we use three im- age quality metrics, such as Peak-Signal-To-Noise ratio (PSNR), Structural Similarity (SSIM) and Normalized root-mean-square error (NRMSE) Figure 65, 48 and 66 show their PSNRs, SSIMs and NRMSEs error graphs, respectively. Additionally, Figure 50 shows the representa- tive reconstruction of the brain and chest test sets, respectively, using various reconstruction methods at different sampling rates (10% and 30%) and their 10×magnified error plots using a jet color map (blue: low, red: high error). Overall, our methods (ReconGAN and RefineGAN) are able to reconstruct images with better PSNRs, SSIMs and NRMSEs. Note that we used the identical generator and discriminator networks (i.e., the same number of neurons) for Sin- gleGAN, and our own method for a fair comparison. We observed that our cyclic loss increases the PSNR by around 1dB, and the refinement network further reduces the error to a similar degree. By qualitatively comparing the reconstructed results, we found that deep learning-based methods generate more natural images than dictionary-based methods. For example, CSCMRI and DLMRI produce cartoon-like piecewise linear images with sharp edges, which is mostly due to sparsity enforcement. In comparison, our method generates results that are much closer to full reconstructions while edges are still preserved; in addition, noise is significantly reduced.
Note also that, comparing to the other CS-MRI methods, our method can generate superior results especially at extremely low sampling rates (as low as 10%, see Figure 50).
Figure 51: Image quality comparison on the knees dataset (top 2 rows: magnitudes, and bottom 2 rows: phases) at a sampling rate 10% : Reconstruction images and zoom-in results
Figure 52: NRMSEs evaluation on the knees test set at sampling rate 20% with various masks